The whole of opposition is comprehended in _two facts_ which are based upon _one principle_. This is the principle: _Whatever may be said of the entire class may be said of a part of that class._ To put it in another way: Whatever is affirmed of all may be affirmed of some, or, Whatever is denied of all may be denied of some. To illustrate: Accepted truth: All planets rotate. (A) Accepted inference: Some planets rotate. (I) or Accepted truth: No planet is a sun. (E) Accepted inference: Some planets are not suns. (O) These are the two facts: First, _a particular affirmative may be derived from a universal affirmative_. Second, _a particular negative may be derived from a universal negative_. Or, more briefly: _An I may be derived from an A, and an O from an E_. SQUARE OF OPPOSITION. Illustration: ( ‡ Square of Opposition) Aristotle represented the relations of the four logical propositions by what is termed the _square of opposition_. Viewed from the standpoint of the square, the relations may be summed up as follows: 1. _Contrary Propositions._ _Why so named._ As related to each other, A and E are said to be contrary because they seem to express _contrariety_ to the greatest degree. _Relation stated._ If one is true, the other must be false, but both may be false. _Illustrations._ (1) If one is true, the other must be false; e. g., if A is true, as “All metals are elements,” then E is false, as “No metals are elements.” Or, if E is true, as “No birds are quadrupeds,” then A is false, as “All birds are quadrupeds.” (2) Both may be false. If A is false, as “All men are wise,” then E may be false, as “No men are wise.” 2. _Subcontrary Propositions._ _Why so named._ Propositions I and O are said to be related to each other in a subcontrary manner because they are contrary as to each other and “_under_” their universals A and E. _Relation stated._ If one is false, the other must be true, or, both may be true. _Illustrations._ (1) If one is false, the other must be true. If I is false, as “Some metals are compounds,” then, O is true, as “Some metals (at least) are not compounds.” Or, if O is false, as “Some metals are not elements,” then I is true, as “Some metals are elements.” (2) Both may be true. If I is true, as “Some men are wise,” then O also may be true, as “Some men are not wise.” 3. _Subalterns._ _Why so named._ Etymologically considered subaltern means _under the one_, thus proposition I is under A, and O is under E. _Relation stated._ _First Relation._ Subalterns are related to each other as are the universals and particulars; hence, (1) If the universal is true, the particular under it is also true; while if the particular is true, the corresponding universal may, or, may not, be true. _Illustrations._ (a) If the universal is true, the particular under it is true.